Geometric Sequence with Normal Distribution ProblemThe running time (in seconds) of an algorithm on a data set is approximately normally distributed with mean 3 and variance 0.25.a. What is the probability that the running time of a run selected at random will exceed 2.6 seconds?Answer for (a): I've computed this and found it to be p = 0.7881..b. What is the probability that the running time of exactly one of four randomly selected runs will exceed 2.6 seconds?Answer for (b): Not sure, I know it's a geometric sequence and I believe the formula that I need to use to be p ( 1 − p ) 3 , thus giving me 0.7881 ( 1 − 0.7881 ) 3 however this was marked incorrect. I'm trying to figure out why, can someone explain my error and how to arrive at the correct solution?

Question

Geometric Sequence with Normal Distribution ProblemThe running time (in seconds) of an algorithm on a data set is approximately normally distributed with mean 3 and variance 0.25.a. What is the probability that the running time of a run selected at random will exceed 2.6 seconds?Answer for (a): I&#039;ve computed this and found it to be   p  =  0.7881..b. What is the probability that the running time of exactly one of four randomly selected runs will exceed 2.6 seconds?Answer for (b): Not sure, I know it&#039;s a geometric sequence and I believe the formula that I need to use to be   p  (  1  −  p      )    3  , thus giving me   0.7881  (  1  −  0.7881      )    3   however this was marked incorrect. I&#039;m trying to figure out why, can someone explain my error and how to arrive at the correct solution?

nuramaaji2000fh · Accepted Answer

Step 1You have 4 choices for which run will exceed 2.6 seconds. So your answer should be   4  p  (  1  −  p      )    3   instead of   p  (  1  −  p      )    3  .Step 2You basically calculated the probability that a pre-determined run will exceed 2.6 seconds, and the other 3 runs are less than 2.6 seconds.